US6111834A - Data storage system having efficient block code implementation - Google Patents
Data storage system having efficient block code implementation Download PDFInfo
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- US6111834A US6111834A US09/020,874 US2087498A US6111834A US 6111834 A US6111834 A US 6111834A US 2087498 A US2087498 A US 2087498A US 6111834 A US6111834 A US 6111834A
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B5/00—Recording by magnetisation or demagnetisation of a record carrier; Reproducing by magnetic means; Record carriers therefor
- G11B5/012—Recording on, or reproducing or erasing from, magnetic disks
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
- G11B20/10—Digital recording or reproducing
- G11B20/14—Digital recording or reproducing using self-clocking codes
- G11B20/1403—Digital recording or reproducing using self-clocking codes characterised by the use of two levels
- G11B20/1423—Code representation depending on subsequent bits, e.g. delay modulation, double density code, Miller code
- G11B20/1426—Code representation depending on subsequent bits, e.g. delay modulation, double density code, Miller code conversion to or from block codes or representations thereof
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B5/00—Recording by magnetisation or demagnetisation of a record carrier; Reproducing by magnetic means; Record carriers therefor
- G11B5/02—Recording, reproducing, or erasing methods; Read, write or erase circuits therefor
- G11B5/09—Digital recording
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
- G11B20/10—Digital recording or reproducing
- G11B20/14—Digital recording or reproducing using self-clocking codes
- G11B20/1403—Digital recording or reproducing using self-clocking codes characterised by the use of two levels
- G11B20/1423—Code representation depending on subsequent bits, e.g. delay modulation, double density code, Miller code
- G11B20/1426—Code representation depending on subsequent bits, e.g. delay modulation, double density code, Miller code conversion to or from block codes or representations thereof
- G11B2020/1446—16 to 17 modulation
Definitions
- the present invention relates to disc drives. More particularly, the present invention relates to block codes used in data channels of disc drives.
- a typical disc drive includes one or more magnetic discs mounted for rotation on a hub or spindle.
- a typical disc drive also includes a transducer supported by an air bearing which flies above each magnetic disc. The transducer and the air bearing are collectively referred to as a data head.
- a drive controller is conventionally used for controlling the disc drive based on commands received from a host system. The drive controller controls the disc drive to retrieve information from the magnetic discs and to store information on the magnetic discs.
- An electromechanical actuator operates within a negative feedback, closed-loop servo system.
- the actuator moves the data head radially over the disc surface for track seek operations and holds the transducer directly over a track on the disc surface for track following operations.
- Information is typically encoded and stored in concentric tracks on the surface of magnetic discs by providing a write signal to the data head to encode flux reversals on the surface of the magnetic disc representing the data to be stored.
- the drive controller controls the electromechanical actuator so that the data head flies above the magnetic disc, sensing the flux reversals on the magnetic disc, and generating a read signal based on those flux reversals.
- the read signal is typically conditioned and then decoded by a read channel or the drive controller to recover data represented by flux reversals stored on the magnetic disc, and consequently represented in the read signal provided by the data head.
- a communication channel represented by such a disc drive includes an encoder which encodes user input data, the data head, the medium (e.g., the magnetic or optical disc), preconditioning logic (such as amplifiers, filters, a gain loop, a sampler, a timing loop, and clock generation), a data detector, and a decoder for decoding the detected data to provide an output indicative of estimated user data.
- the medium e.g., the magnetic or optical disc
- preconditioning logic such as amplifiers, filters, a gain loop, a sampler, a timing loop, and clock generation
- a data detector e.g., a data detector
- decoder for decoding the detected data to provide an output indicative of estimated user data.
- Block coding techniques are typically used in disc drives and are well suited for correcting burst errors and imposing certain properties (constraints) in the encoded data which are useful in subsequent data processing.
- One type of block code is a Run-Length-Limited (RLL) code which limits the number of flux transitions which occur in a sequence.
- RLL Run-Length-Limited
- a block encoder and decoder having a rate of m/n for encoding data in blocks can be implemented using two tables which are related to the size of the block.
- the encoder is formed by a table having 2 m ⁇ n data entries and the decoder may be formed by a table having 2 n ⁇ m data entries.
- the encoder is formed by a table having 2 m ⁇ n data entries
- the decoder may be formed by a table having 2 n ⁇ m data entries.
- these tables become prohibitively large and cannot be practically implemented in a disc drive storage system.
- One approach which is used to implement block encoding in systems having relatively large values of m and n is to only encode a portion of each data word. The remainder of the data word is left unencoded.
- a common technique to implement a 16/17 rate code is to leave the first eight bits unencoded and encode the remaining eight bits into nine bits. In this manner, the complexity of the encoder is comparable to that of a 8/9 rate encoder.
- the disadvantage is that eight bits are passed through unencoded and cannot be used to impose code constraints, such as run length limits.
- the present invention provides a solution to this and other problems, and offers advantages over the prior art.
- the present invention relates to storage systems having block encoders which solve the above-mentioned problem.
- a storage device includes a storage medium and a write element positioned adjacent the storage medium to write information to the storage medium in response to a write signal input.
- a data input is provided which has a plurality of data input bits.
- a first encoder is coupled to the data input and includes a first encoded data output as a function of a first portion of the plurality of data input bits along with a state output. The first encoded data output is coupled to the write signal input of the write element.
- a second encoder is coupled to the data input and includes a second encoded data output as a function of a second portion of the plurality of data input bits and the state output. The second encoded data output is coupled to the write signal input of the write element.
- a storage device in another embodiment, includes a storage medium and a read element positioned adjacent the storage medium to read information to the storage medium and provide a read signal output.
- a first decoder is coupled to the read element and includes a first decoded data output as a function of a first portion of the read signal output and a state output. The first decoded data output is coupled to a system output.
- a second decoder is coupled to the read element and including a second decoded data output as a function of the read signal output and as a function of the state output. The second decoded data output is coupled to the system output.
- FIG. 1 is a simplified block diagram of a data storage system in accordance with the present invention.
- FIG. 2 is a diagram of a prior art block encoder.
- FIG. 3 is a diagram of a prior art block decoder.
- FIG. 4 is a diagram of a block encoder in accordance with one embodiment of the present invention.
- FIG. 5 is a diagram of a block decoder in accordance with one embodiment of the present invention.
- FIG. 6 is a block diagram of an encoder in accordance with a second embodiment of the present invention.
- FIG. 7 is a block diagram of a decoder in accordance with a second embodiment of the present invention.
- System 100 may be any type of storage device including magnetic, optical, magneto optical, etc.
- System 100 includes disc 102, read circuitry 104 and write circuitry 106 coupled to a transducing head 108 through switch 110.
- Transducing head 108 is positioned over a data surface of disc 102 and in one preferred embodiment comprises a head for reading and writing magnetically encoded information.
- Information received from input circuitry 112 is written onto disc 102 by write circuitry 106 which applies a write signal to transducing element 108.
- a signal is generated by transducing head 108 which is representative of a data signal stored on disc 102 and is provided to read circuitry 104.
- Read circuitry 104 decodes data carried in the data signal and provides an output through output circuitry 114.
- Write circuitry 106 includes encoding section 120 and amplification circuitry 122.
- Encoding section 120 is shown generally with a block encoder 124 and a PR4 precoder 126.
- Read circuitry 104 includes amplifier 130 and decoding section 131.
- Decoding section 131 generally includes a Partial Response Maximum Likelihood (PRML) detection 132 and a block decoder 134 in accordance with the present invention.
- Block encoder 124 and block decoder 134 are in accordance with the present invention and are described below in greater detail.
- Class 4 Partial Response (PR4) precoder 126 provides encoding to the data which is useful for PRML channels.
- Block encoder 124 and block decoder 134 operate in accordance with the present invention and efficiently encodes and decodes all bits of long data words without the large look-up tables required by the prior art.
- block encoder 124 and block decoder 134 partition the data word to reduce the complexity of the encoding and decoding.
- the technique is useful for implementing higher rate codes such as codes with a 16/17 rate or greater, and imposing properties on the code that are useful when followed by a PR4 precoder 126 for use with PRML channels.
- code constraints are imposed which have the following properties:
- g global Run-Length-Limited (RLL) constrains. Maximum run of 0's anywhere in the encoded sequence.
- I interleave RLL constraint. Maximum run of 0's per interleave.
- Minimum code energy Number of one's in the encoded pattern. This is an indication of the amount of timing information on each codeword. With the preferred embodiment, the following constraints may be obtained:
- FIGS. 2 and 3 are block diagrams of prior art 16/17 rate block encoder and decoder, respectively.
- the 16/17 rate block encoder of FIG. 2 receives 16 data bits of input (D0-D15) and provides a 17 code bit output (bits C0-C16) using a 2 16 ⁇ 17 look-up table.
- 17 data bits (C0-C16) are decoded using a 2 17 ⁇ 16 look-up table into 16 data bits (D0-D15).
- This prior art approach provides the desired code output, however, it requires relatively large look-up tables which are inefficient and may be impractical in most systems.
- FIG. 4 is a diagram of a block encoder 124 in accordance with one embodiment of the present invention.
- Block encoder 124 includes a first (Part A) encoder 152 and a second (Part B) encoder 154.
- the preferred embodiment partitions the input data into two parts.
- Data bits A0-A7 i.e., 8 bits
- Data bits B0-B7 i.e., 8 bits
- Encoder 152 provides a first encoded data output having bits Y0-Y6 which correspond to bits C0-C6 of FIG. 2.
- encoder 154 provides an encoded data output signal having bits Z0-Z9 which correspond to bits C7-C16 of FIG. 2.
- Encoder 152 provides a state number output 156 to encoder 154.
- Each entry in the table of encoder 152 is a 7 bit codeword along with a state number of two bits which is communicated to encoder 154.
- there are 3 ⁇ 127 381 possible combinations of codewords for encoder 152 and the corresponding state number.
- some Part A codewords in encoder 152 may be eliminated and/or some Part B state and Part A codewords may be disallowed.
- FIG. 5 is a diagram of block decoder 134.
- Decoder 134 includes a first (Part B) decoder 162 and a second (Part A) decoder 164.
- Decoder 162 receives 10 data bits (Z0-Z9) and provides 8 decoded data bits (B0-B7) and a state number output 166.
- Decoder 164 receives 7 data bits (Y0-Y6) along with the state number from decoder 162 and provides an 8 data bit output (A0-A7).
- decoder 162 is a table of 2 10 ⁇ (8+2) (8 bits of data and 2 bits of state) and decoder 164 is a table of 3 ⁇ 2 7 ⁇ 8.
- One important property of a preferred decoder implementation is that an error in bits Y0-Y6 will only affect a single byte (decoded bits A0-A7) of the decoded data. This is preferred because it limits the error propagation of the decoder to a maximum of 3 bytes. Error events that are 8 bits or less in length are guaranteed to affect only 3 bytes of data. Longer error events, for example one that starts in part B of one codeword and ends in part B of the next codeword, can be restricted by eliminating some part A patterns. For an embodiment using EPR4, it is sufficient to eliminate all part A patterns that are all zero in either interleave.
- the sequence of the part A codewords and the part B states can then be constrained to guarantee that the combined code energy (the sum of the code energy of part A and part B) is also 7 or greater, as shown below in Table 3:
- a minimum code energy (or Hamming weight) of 7 can also be achieved if the minimum code energy of each part B codeword is 4 and the minimum code energy of each part A codeword is 3.
- Table 4 is a table for use as encoder 152 of FIG. 4 and shows the data input along with the corresponding codeword output (CW) and state number output (Nx St).
- Table 5 is the encoding table for encoder 154 of FIG. 4 when state number 156 is zero.
- Table 6 is the encoding table when state number 156 is 1.
- Table 7 is the encoding table when state number 156 is 2.
- FIG. 6 shows a block diagram for an encoder 200 for producing a rate 16/17 code with minimum Hamming weight of 7 and a run-length-limited constraint of 6 for the entire encoded sequence and 6 for each interleave in the sequence.
- Encoder 200 is divided into two parts, part A and part B. Part A consists of code tester (A) 202 and encoder (A) 204 and part B consists of code tester (B) 206 and encoder (B) 208.
- Encoder (A) 204 receives the 8 most significant bits (D 15 -D 8 ) of a 16 bit input data word (D 15:0 ) along input bus 220. These 8 bits are denoted as A 7:0 in encoder (A) 204, which is shorthand for a string of 8 bits: A 7 A 6 A 5 A 4 A 3 A 2 A 1 A 0 . Of the 8 bits received by encoder (A) 204, code tester (A) 202 receives the least significant 7 bits, denoted as WA 6:0 in code tester (A) 202, along bus 222.
- Code tester (A) 202 produces output TA 203 which is input to encoder (A) 204. Based on TA 203 and inputs A 7:0 , encoder (A) 204 produces 7 code bits Y 6:0 on output bus 210. Encoder (A) 204 also produces three state variables S 0 , S 1 and S 2 and two part B bits WB 8 and WB 9 .
- Part B bits WB 8 and WB 9 are input to code tester (B) 206, along lines 216 and 218, respectively.
- Code tester (B) 206 also receives the least significant 8 bits (D 7 -D 0 ) of the input data word along input data bus 224. These bits are denoted as input bits WB 7:0 in code tester (B) 206. Based on inputs WB 7:0 , WB 8 and WB 9 , code tester (B) 206 produces an output TB 214 which is input to encoder (B) 208.
- encoder (B) 208 receives state variables S 0 , S 1 and S 2 along lines 228, 230 and 232, respectively, and the least significant 8 bits (D 7 -D 0 ) of the input data word along input bus 226. Within encoder (B) 208, the least significant 8 bits of the input data word are denoted as B 7:0 . Based upon all of the input values, encoder (B) 208 produces 10 output code bits Z 9:0 along output bus 212.
- code tester (A) 202 code tester (A) 202, encoder (A) 204, code tester (B) 206, and encoder (B) 208 is described below using the following symbols:
- Code tester (A) 202 produces output TA 203 based upon inputs WA 6:0 using the following equations:
- Encoder (A) 204 produces output 210 (Y 6:0 ) using input bits A 7:0 and TA 203 in equations 7 through 29 below.
- Encoder (A) 204 produces state variables S 0 , S 1 and S 2 using the following equations:
- Code tester (B) 206 produces output TB 214 using input bits WB 7:0 of the input data word and bits WB 8 and WB 9 from encoder (A) 204 in the following equations:
- Encoder (B) 208 produces output bits 212 (Z 9:0 ) using the least significant 8 bits of the input data word (B 7:0 ), the three state variables S 0 , S 1 and S 2 and TB 214 in the following equations:
- the 7 output bits 210 (Y 6:0 ) and the 10 output bits 212 (Z 9:0 ) are concatenated together to form a 17 bit codeword.
- FIG. 7 is a block diagram of a decoder 250 for decoding the codewords produced by encoder 200.
- Decoder 250 includes a part A and a part B, where part A includes code tester (A) 252 and decoder (A) 254, and part B includes code tester (B) 256 and decoder (B) 258.
- code tester (B) 256 receives the same 10 code bits along input bus 262, but denotes the 10 bits as WB 9:0 . Code tester (B) 256 uses these input bits to produce output TB 264 using equations 35 through 42 described above. Thus, code tester (B) 256 contains the same combinational logic as code tester (B) 206 of FIG. 6.
- the code tester circuit 206 may be shared by the encoder (FIG. 6) and the decoder (FIG. 7).
- Output TB 264 is input to decoder (B) 258 along with the 10 least significant bits of the codeword (Z 9:0 ) Decoder (B) 258 uses these inputs to produce state outputs S 0 ,S 1 and S 2 , along lines 266, 268 and 270, respectively, invalid codeword indicator FB on line 272, and the 8 least significant bits (B 7:0 ) of the recovered data word along output bus 274.
- Invalid codeword indicator FB is simply the inverse of TB 264and variables S 0 , S 1 and S 2 and recovered data bits B 7:0 are produced using the following equations:
- Code tester (A) 252 receives the 7 most significant bits of the codeword, which are represented as WA 6:0 in code tester (A) 252, along input bus 276. Code tester (A) 252 uses equations 1 through 6 described above together with the input bits to produce output TA 278, which is provided to decoder (A) 254. Thus, code tester (A) 252 contains the same combinational logic as code tester (A) 202 of FIG. 6.
- Decoder (A) 254 also receives the most significant 7 bits (Y 6:0 ) of the codeword along input bus 280 and state variables S 0 , S 1 and S 2 from decoder (B) 258 along lines 266, 268, and 270, respectively. Decoder (A) 254 uses these input values to produce the 8 most significant bits (A 7:0 ) of the recovered data word and an invalid codeword indicator FA along output bus 282 and line 284, respectively.
- Invalid codeword indicator FA is simply the inverse of TA 278 from code tester (A) 252. Recovered data bits A 7:0 are determined using the following equations:
- the preferred embodiment includes a storage device 100 having a storage medium 102 and a write element 108 positioned adjacent the storage medium 102 to write information to the storage medium 102 in response to a write signal input.
- the device 100 also includes a data input 112 providing a plurality of data input bits to a first block encoder 152.
- the first block encoder 152 provides a first encoded data output to the write element 108 as a function of a portion of the data input 112.
- the first encoder also provides a state number output 156 as a function of the data input.
- the second encoder 154 also couples the data input 112 and provides a second encoded output to the write element 108 as a function of a portion of the data input 112 and as a function of the state number output 156. Further, the first and second encoder output may be provided to a PRML precoder 126 which responsively provides the write signal to the write element 108.
- storage device 100 includes read element 108 which reads information from storage medium 102 and responsively provides a read signal output.
- a first decoder 162 is coupled to the read element and provides a state number output 166 and a first decoded data output as a function of a portion of a read signal output from the read element 108.
- the first decoded output is provided to a system data output 114.
- a second decoder couples to the read element 108 and provides a second decoded data output 114 as a function of the read signal output and as a function of the state number output 166.
- the second decoded output is also provided to the data output 114.
- a PRML detector 132 may also be provided between read element 108 and decoders 162 and 164.
- the present encoder/decoder greatly reduces the number of entries in a table of the type used in encoding and decoding.
- the encoder/decoder provides a plurality of block encoding/decoding tables in which an output from one table is used as an input to another table. This allows the overall number of data entries to be reduced without sacrificing the constraints placed on the code.
- the encoder/decoder may be implemented as appropriate including software or hardware implementations. Further, the particular codes, number of tables, number of state, etc., may change for any particular application.
- the encoder/decoder may use other techniques as desired including algorithm based or adaptive data translation techniques. Aspects of the invention include the division of codewords into two unequal parts and implementation of state dependent encoding/decoding with a different number of states for each pair. Further, each part of the decoder input has the same length.
- the code tester can be used to reduce logic count because the input data pattern can be used directly as the codeword if it satisfies the code constraints.
- the code tester checks the constraints and sends a signal to the encoder if the input word directly satisfies the constraints.
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Abstract
A storage device includes a storage medium, write element and a data input. A first encoder provides an encoded data output as a function of a first portion of the data input. The first encoder also provides a state output. A second encoder provides a second encoded data output as a function of the plurality of data input and as a function of the state output. The first and second data outputs are coupled to the write element for writing information onto the storage medium. In addition, a similar technique is used for a block decoder.
Description
The present invention claims priority to Provisional Application Ser. No. 60/054,739, filed Aug. 11, 1997 and entitled EFFICIENT BLOCK CODE IMPLEMENTATION.
The present invention relates to disc drives. More particularly, the present invention relates to block codes used in data channels of disc drives.
A typical disc drive includes one or more magnetic discs mounted for rotation on a hub or spindle. A typical disc drive also includes a transducer supported by an air bearing which flies above each magnetic disc. The transducer and the air bearing are collectively referred to as a data head. A drive controller is conventionally used for controlling the disc drive based on commands received from a host system. The drive controller controls the disc drive to retrieve information from the magnetic discs and to store information on the magnetic discs.
An electromechanical actuator operates within a negative feedback, closed-loop servo system. The actuator moves the data head radially over the disc surface for track seek operations and holds the transducer directly over a track on the disc surface for track following operations.
Information is typically encoded and stored in concentric tracks on the surface of magnetic discs by providing a write signal to the data head to encode flux reversals on the surface of the magnetic disc representing the data to be stored. In retrieving data from the disc, the drive controller controls the electromechanical actuator so that the data head flies above the magnetic disc, sensing the flux reversals on the magnetic disc, and generating a read signal based on those flux reversals. The read signal is typically conditioned and then decoded by a read channel or the drive controller to recover data represented by flux reversals stored on the magnetic disc, and consequently represented in the read signal provided by the data head.
A communication channel represented by such a disc drive includes an encoder which encodes user input data, the data head, the medium (e.g., the magnetic or optical disc), preconditioning logic (such as amplifiers, filters, a gain loop, a sampler, a timing loop, and clock generation), a data detector, and a decoder for decoding the detected data to provide an output indicative of estimated user data.
Generally, there are two types of encoding techniques used in communication channels. These are block encoding and convolution encoding techniques. Block coding techniques are typically used in disc drives and are well suited for correcting burst errors and imposing certain properties (constraints) in the encoded data which are useful in subsequent data processing. One type of block code is a Run-Length-Limited (RLL) code which limits the number of flux transitions which occur in a sequence. Advanced data storage systems frequently use error-correction encoding concatenated with RLL encoding.
A block encoder and decoder having a rate of m/n for encoding data in blocks can be implemented using two tables which are related to the size of the block. The encoder is formed by a table having 2m ×n data entries and the decoder may be formed by a table having 2n ×m data entries. However, for large values of m and n, these tables become prohibitively large and cannot be practically implemented in a disc drive storage system.
One approach which is used to implement block encoding in systems having relatively large values of m and n is to only encode a portion of each data word. The remainder of the data word is left unencoded. For example, a common technique to implement a 16/17 rate code is to leave the first eight bits unencoded and encode the remaining eight bits into nine bits. In this manner, the complexity of the encoder is comparable to that of a 8/9 rate encoder. The disadvantage is that eight bits are passed through unencoded and cannot be used to impose code constraints, such as run length limits.
The present invention provides a solution to this and other problems, and offers advantages over the prior art.
The present invention relates to storage systems having block encoders which solve the above-mentioned problem.
In accordance with one embodiment of the invention, a storage device includes a storage medium and a write element positioned adjacent the storage medium to write information to the storage medium in response to a write signal input. A data input is provided which has a plurality of data input bits. A first encoder is coupled to the data input and includes a first encoded data output as a function of a first portion of the plurality of data input bits along with a state output. The first encoded data output is coupled to the write signal input of the write element. A second encoder is coupled to the data input and includes a second encoded data output as a function of a second portion of the plurality of data input bits and the state output. The second encoded data output is coupled to the write signal input of the write element.
In another embodiment, a storage device includes a storage medium and a read element positioned adjacent the storage medium to read information to the storage medium and provide a read signal output. A first decoder is coupled to the read element and includes a first decoded data output as a function of a first portion of the read signal output and a state output. The first decoded data output is coupled to a system output. A second decoder is coupled to the read element and including a second decoded data output as a function of the read signal output and as a function of the state output. The second decoded data output is coupled to the system output.
These and various other features as well as advantages which characterize the present invention will be apparent upon reading of the following detailed description and review of the associate drawings.
FIG. 1 is a simplified block diagram of a data storage system in accordance with the present invention.
FIG. 2 is a diagram of a prior art block encoder.
FIG. 3 is a diagram of a prior art block decoder.
FIG. 4 is a diagram of a block encoder in accordance with one embodiment of the present invention.
FIG. 5 is a diagram of a block decoder in accordance with one embodiment of the present invention.
FIG. 6 is a block diagram of an encoder in accordance with a second embodiment of the present invention.
FIG. 7 is a block diagram of a decoder in accordance with a second embodiment of the present invention.
Referring now to FIG. 1, a simplified block diagram of a disc drive storage system 100 in accordance with the present invention is shown. System 100 may be any type of storage device including magnetic, optical, magneto optical, etc. System 100 includes disc 102, read circuitry 104 and write circuitry 106 coupled to a transducing head 108 through switch 110. Transducing head 108 is positioned over a data surface of disc 102 and in one preferred embodiment comprises a head for reading and writing magnetically encoded information. Information received from input circuitry 112 is written onto disc 102 by write circuitry 106 which applies a write signal to transducing element 108. During readback, a signal is generated by transducing head 108 which is representative of a data signal stored on disc 102 and is provided to read circuitry 104. Read circuitry 104 decodes data carried in the data signal and provides an output through output circuitry 114.
Using known data encoding techniques, it is possible to record information on disc 102 such that errors may be detected, and in some instances corrected, during readback of the stored information. Write circuitry 106 includes encoding section 120 and amplification circuitry 122. Encoding section 120 is shown generally with a block encoder 124 and a PR4 precoder 126. Read circuitry 104 includes amplifier 130 and decoding section 131. Decoding section 131 generally includes a Partial Response Maximum Likelihood (PRML) detection 132 and a block decoder 134 in accordance with the present invention. Block encoder 124 and block decoder 134 are in accordance with the present invention and are described below in greater detail. Class 4 Partial Response (PR4) precoder 126 provides encoding to the data which is useful for PRML channels.
In implementing a block code in accordance with the present invention, various code constraints can be imposed. In one preferred embodiment, code constraints are imposed which have the following properties:
g: global Run-Length-Limited (RLL) constrains. Maximum run of 0's anywhere in the encoded sequence.
I: interleave RLL constraint. Maximum run of 0's per interleave.
Maximum error propagation: Number of bytes in error as a result of a single minimum distance error event.
Minimum code energy: Number of one's in the encoded pattern. This is an indication of the amount of timing information on each codeword. With the preferred embodiment, the following constraints may be obtained:
TABLE 1
______________________________________
Maximum Error
Minimum Code
g i Propagation (Bytes)
Energy
______________________________________
4 7 3 4
5 6 3 6
6 6 3 7
______________________________________
FIGS. 2 and 3 are block diagrams of prior art 16/17 rate block encoder and decoder, respectively. The 16/17 rate block encoder of FIG. 2 receives 16 data bits of input (D0-D15) and provides a 17 code bit output (bits C0-C16) using a 216 ×17 look-up table. Similarly, as shown in FIG. 3, 17 data bits (C0-C16) are decoded using a 217 ×16 look-up table into 16 data bits (D0-D15). This prior art approach provides the desired code output, however, it requires relatively large look-up tables which are inefficient and may be impractical in most systems.
FIG. 4 is a diagram of a block encoder 124 in accordance with one embodiment of the present invention. Block encoder 124 includes a first (Part A) encoder 152 and a second (Part B) encoder 154. The preferred embodiment partitions the input data into two parts. Data bits A0-A7 (i.e., 8 bits) which correspond to bits D8-D15 of FIG. 2 are provided to encoder 152. Data bits B0-B7 (i.e., 8 bits) which correspond to bits D0-D7 of FIG. 2 are provided to encoder 154. Encoder 152 provides a first encoded data output having bits Y0-Y6 which correspond to bits C0-C6 of FIG. 2. Similarly, encoder 154 provides an encoded data output signal having bits Z0-Z9 which correspond to bits C7-C16 of FIG. 2.
Encoder 152 provides a state number output 156 to encoder 154. Encoder 154 includes a table having three groups of 10 bit codewords each group is assigned a state number (0, 1 or 2). There are 256 codewords in each 10 bit group. Thus, there are only 3×256=768 codewords out of 1024 possible codewords which are used by encoder 154. Preferably, these unused codewords are chosen to provide preferred code properties in conjunction with encoder 152.
Each entry in the table of encoder 152 is a 7 bit codeword along with a state number of two bits which is communicated to encoder 154. There are 127 possible non-zero values for the codeword of encoder 152. Thus, there are 3×127=381 possible combinations of codewords for encoder 152 and the corresponding state number. However, as only 256 entries are required for encoder 152, some Part A codewords in encoder 152 may be eliminated and/or some Part B state and Part A codewords may be disallowed.
FIG. 5 is a diagram of block decoder 134. Decoder 134 includes a first (Part B) decoder 162 and a second (Part A) decoder 164. Decoder 162 receives 10 data bits (Z0-Z9) and provides 8 decoded data bits (B0-B7) and a state number output 166. Decoder 164 receives 7 data bits (Y0-Y6) along with the state number from decoder 162 and provides an 8 data bit output (A0-A7). For the examples shown, decoder 162 is a table of 210 ×(8+2) (8 bits of data and 2 bits of state) and decoder 164 is a table of 3×27 ×8.
One important property of a preferred decoder implementation is that an error in bits Y0-Y6 will only affect a single byte (decoded bits A0-A7) of the decoded data. This is preferred because it limits the error propagation of the decoder to a maximum of 3 bytes. Error events that are 8 bits or less in length are guaranteed to affect only 3 bytes of data. Longer error events, for example one that starts in part B of one codeword and ends in part B of the next codeword, can be restricted by eliminating some part A patterns. For an embodiment using EPR4, it is sufficient to eliminate all part A patterns that are all zero in either interleave.
It is also preferable to reduce the probability of propagating errors to 2 bytes by making the state number determination independent of any bits which are located near the end of the codeword. For example, if the state number can be uniquely determined by bits Z5-Z9, then any errors in bits Z0-Z4 will not affect the decoding of part A. In this way, error events of 6 bits or less can only corrupt 2 bytes and error events of 13 bits or less are guaranteed to only affect 3 bytes of data.
It is also possible to use the sequence of codewords included in the encoding table of encoder 152 to ensure a minimum code energy for each word. Further, the grouping of the part B codewords should also take into account to ensure a minimum code energy. It is possible to have a minimum code energy state as given in Table 2:
TABLE 2 ______________________________________ State Part B Minimum Code Energy ______________________________________ 0 3 1 4 2 5 ______________________________________
The sequence of the part A codewords and the part B states can then be constrained to guarantee that the combined code energy (the sum of the code energy of part A and part B) is also 7 or greater, as shown below in Table 3:
TABLE 3
______________________________________
Part A Code Energy
Valid State Transitions
______________________________________
2 2
3 1 or 2
4 0, 1 or 2
______________________________________
As another example, a minimum code energy (or Hamming weight) of 7 can also be achieved if the minimum code energy of each part B codeword is 4 and the minimum code energy of each part A codeword is 3.
In one preferred embodiment, a 16/17 (0, 6/6) code with a minimum Hamming weight of 7 is implemented. Table 4 is a table for use as encoder 152 of FIG. 4 and shows the data input along with the corresponding codeword output (CW) and state number output (Nx St).
TABLE 4
__________________________________________________________________________
State Diagram of 7-bit codeword mapping for 16/17 (0, 6/6) code [Min Hwt
= 3]
Data
CW Nx St
Data
CW Nx St
Data
CW Nx St
Data
CW Nx St
__________________________________________________________________________
00 0E S0 40 4E S0 80 0F S0 C0 4F S0
01 16 S0 41 2B S0 81 17 S0 C1 6B S0
02 26 S0 42 3A S0 82 27 S0 C2 7A S0
03 36 S0 43 43 S1 83 37 S0 C3 43 S2
04 46 S0 44 2D S0 84 47 S0 C4 6D S0
05 56 S0 45 39 S0 85 57 S0 C5 79 S0
06 66 S0 46 46 S1 86 67 S0 C6 46 S2
07 76 S0 47 47 S1 87 77 S0 C7 47 S2
08 61 S0 48 25 S0 88 71 S0 C8 35 S0
09 62 S0 49 49 S1 89 72 S0 C9 49 S2
0A 63 S0 4A 4A S1 8A 73 S0 CA 4A S2
0B 0B S1 4B 4B S1 8B 0B S2 CB 4B S2
0C 65 S0 4C 4C S1 8C 75 S0 CC 4C S2
0D 0D S1 4D 4D S1 8D 0D S2 CD 4D S2
0E 0E S1 4E 4E S1 8E 0E S2 CE 4E S2
0F 0F S1 4F 4F S1 8F 0F S2 CF 4F S2
10 1E S0 50 5E S0 90 1F S0 D0 5F S0
11 1B S0 51 3B S0 91 5B S0 D1 7B S0
12 1A S0 52 52 S1 92 5A S0 D2 52 S2
13 13 S1 53 53 S1 93 13 S2 D3 53 S2
14 1D S0 54 3D S0 94 5D S0 D4 7D S0
15 19 S0 55 29 S0 95 59 S0 D5 69 S0
16 16 S1 56 56 S1 96 16 S2 D6 56 S2
17 17 S1 57 57 S1 97 17 S2 D7 57 S2
18 23 S0 58 58 S1 98 43 S0 D8 58 S2
19 19 S1 59 59 S1 99 19 S2 D9 59 S2
1A 1A S1 5A 5A S1 9A 1A S2 DA 5A S2
1B 1B S1 5B 5B S1 9B 1B S2 DB 5B S2
1C 1C S1 5C 5C S1 9C 1C S2 DC 5C S2
1D 1D S1 5D 5D S1 9D 1D S2 DD 5D S2
1E 1E S1 5E 5E S1 9E 1E S2 DE 5E S2
1F 1F S1 5F 5F S1 9F 1F S2 DF 5F S2
20 2E S0 60 6E S0 A0 2F S0 E0 6F S0
21 0B S0 61 61 S1 A1 4B S0 E1 61 S2
22 6A S0 62 62 S1 A2 4A S0 E2 62 S2
23 23 S1 63 63 S1 A3 23 S2 E3 63 S2
24 0D S0 64 64 S1 A4 4D S0 E4 64 S2
25 25 S1 65 65 S1 A5 25 S2 E5 65 S2
26 26 S1 66 66 S1 A6 26 S2 E6 66 S2
27 27 S1 67 67 S1 A7 27 S2 E7 67 S2
28 33 S0 68 68 S1 A8 53 S0 E8 68 S2
29 29 S1 69 69 S1 A9 29 S2 E9 69 S2
2A 32 S0 6A 6A S1 AA 52 S0 EA 6A S2
2B 2B S1 6B 6B S1 AB 2B S2 EB 6B S2
2C 2C S1 6C 6C S1 AC 2C S2 EC 6C S2
2D 2D S1 6D 6D S1 AD 2D S2 ED 6D S2
2E 2E S1 6E 6E S1 AE 2E S2 EE 6E S2
2F 2F S1 6F 6F S1 AF 2F S2 EF 6F S2
30 3E S0 70 7E S0 B0 3F S0 F0 7F S0
31 31 S1 71 71 S1 B1 31 S2 F1 71 S2
32 32 S1 72 72 S1 B2 32 S2 F2 72 S2
33 33 S1 73 73 S1 B3 33 S2 F3 73 S2
34 34 S1 74 74 S1 B4 34 S2 F4 74 S2
35 35 S1 75 75 S1 B5 35 S2 F5 75 S2
36 36 S1 76 76 S1 B6 36 S2 F6 76 S2
37 37 S1 77 77 S1 B7 37 S2 F7 77 S2
38 38 S1 78 78 S1 B8 38 S2 F8 78 S2
39 39 S1 79 79 S1 B9 39 S2 F9 79 S2
3A 3A S1 7A 7A S1 BA 3A S2 FA 7A S2
3B 3B S1 7B 7B S1 BB 3B S2 FB 7B S2
3C 3C S1 7C 7C S1 BC 3C S2 FC 7C S2
3D 3D S1 7D 7D S1 BD 3D S2 FD 7D S2
3E 3E S1 7E 7E S1 BE 3E S2 FE 7E S2
3F 3F S1 7F 7F S1 BF 3F S2 FF 7F S2
__________________________________________________________________________
Similarly, Table 5 is the encoding table for encoder 154 of FIG. 4 when state number 156 is zero. Table 6 is the encoding table when state number 156 is 1. Table 7 is the encoding table when state number 156 is 2.
TABLE 5
__________________________________________________________________________
State 0 of 10-bit codewords for 16/17 (0, 6/6) code [Min Hwt = 4]
0 1 2 3 4 5 6 7 8 9 A B C D E F
__________________________________________________________________________
0X 02F
04D
04E
04F
097
096
095
207
03B
03C
039
03A
03F
20D
20E
20F
1X 071
05D
05E
213
067
066
216
217
04B
219
21A
21B
21C
21D
21E
21F
2X 072
06D
06E
06F
087
225
226
227
05B
05C
059
05A
22C
22D
22E
22F
3X 073
231
232
233
234
235
236
237
238
239
23A
23B
23C
23D
23E
23F
4X 074
02D
02E
243
057
056
246
247
063
249
24A
24B
24C
24D
24E
24F
5X 075
03D
252
253
037
036
256
257
258
259
25A
25B
25C
25D
25E
25F
6X 076
261
262
263
264
265
266
267
268
269
26A
26B
26C
26D
26E
26F
7X 077
271
272
273
274
275
276
277
278
279
27A
27B
27C
27D
27E
27F
8X 078
08D
08E
08F
047
285
286
287
06B
06C
069
06A
28C
28D
28E
28F
9X 079
291
292
293
294
295
296
297
298
299
29A
29B
29C
29D
29E
29F
AX 07A
09D
09E
09F
2A4
2A5
2A6
2A7
09B
09C
099
09A
2AC
2AD
2AE
2AF
BX 07B
2B1
2B2
2B3
2B4
2B5
2B6
2B7
2B8
2B9
2BA
2BB
2BC
2BD
2BE
2BF
CX 07C
2C1
2C2
2C3
2C4
2C5
2C6
2C7
2C8
2C9
2CA
2CB
2CC
2CD
2CE
2CF
DX 07D
2D1
2D2
2D3
2D4
2D5
2D6
2D7
2D8
2D9
2DA
2DB
2DC
2DD
2DE
2DF
EX 07E
2E1
2E2
2E3
2E4
2E5
2E6
2E7
2E8
2E9
2EA
2EB
2EC
2ED
2EE
2EF
FX 07F
2F1
2F2
2F3
2F4
2F5
2F6
2F7
2F8
2F9
2FA
2FB
2FC
2FD
2FE
2FF
__________________________________________________________________________
TABLE 6
__________________________________________________________________________
State 1 of 10-bit codewords for 16/17 (0, 6/6) code [Min Hwt = 4]
0 1 2 3 4 5 6 7 8 9 A B C D E F
__________________________________________________________________________
0X 0B5
0B4
0B7
0B6
0C6
0C7
0C9
107
0A5
0A6
0A7
10B
0B1
10D
10E
10F
1X 0D1
0B8
0B9
113
0CA
0CB
116
117
0AC
119
11A
11B
11C
11D
11E
11F
2X 0D2
0BC
0BD
123
0C5
125
126
127
0AD
129
12A
12B
12C
12D
12E
12F
3X 0D3
131
132
133
134
135
136
137
138
139
13A
13B
13C
13D
13E
13F
4X 0D4
0BA
0BB
143
0CC
0CD
146
147
0AE
149
14A
14B
14C
14D
14E
14F
5X 0D5
0B2
152
153
0CE
0CF
156
157
158
159
15A
15B
15C
15D
15E
15F
6X 0D6
161
162
163
164
165
166
167
168
169
16A
16B
16C
16D
16E
16F
7X 0D7
171
172
173
174
175
176
177
178
179
17A
17B
17C
17D
17E
17F
8X 0D8
0BE
0BF
183
0C3
185
186
187
0AF
189
18A
18B
18C
18D
18E
18F
9X 0D9
191
192
193
194
195
196
197
198
199
19A
19B
19C
19D
19E
19F
AX 0DA
1A1
1A2
1A3
1A4
1A5
1A6
1A7
1A8
1A9
1AA
1AB
1AC
1AD
1AE
1AF
BX 0DB
1B1
1B2
1B3
1B4
1B5
1B6
1B7
1B8
1B9
1BA
1BB
1BC
1BD
1BE
1BF
CX 0DC
1C1
1C2
1C3
1C4
1C5
1C6
1C7
1C8
1C9
1CA
1CB
1CC
1CD
1CE
1CF
DX 0DD
1D1
1D2
1D3
1D4
1D5
1D6
1D7
1D8
1D9
1DA
1DB
1DC
1DD
1DE
1DF
EX 0DE
1E1
1E2
1E3
1E4
1E5
1E6
1E7
1E8
1E9
1EA
1EB
1EC
1ED
1EE
1EF
FX 0DF
1F1
1F2
1F3
1F4
1F5
1F6
1F7
1F8
1F9
1FA
1FB
1FC
1FD
1FE
1FF
__________________________________________________________________________
TABLE 7
__________________________________________________________________________
State 2 of 10-bit codewords for 16/17 (0, 6/6) code [Min Hwt = 4]
0 1 2 3 4 5 6 7 8 9 A B C D E F
__________________________________________________________________________
0X 0E1
0E4
0E2
303
0E8
0EC
306
307
0E3
309
30A
30B
30C
30D
30E
30F
1X 0F1
0E5
312
313
0E9
0ED
316
317
318
319
31A
31B
31C
31D
31E
31F
2X 0F2
321
322
323
324
325
326
327
328
329
32A
32B
32C
32D
32E
32F
3X 0F3
331
332
333
334
335
336
337
338
339
33A
33B
33C
33D
33E
33F
4X 0F4
0E6
342
343
0EA
0EE
346
347
348
349
34A
34B
34C
34D
34E
34F
5X 0F5
0E7
352
353
0EB
0EF
356
357
358
359
35A
35B
35C
35D
35E
35F
6X 0F6
361
362
363
364
365
366
367
368
369
36A
36B
36C
36D
36E
36F
7X 0F7
371
372
373
374
375
376
377
378
379
37A
37B
37C
37D
37E
37F
8X 0F8
381
382
383
384
385
386
387
388
389
38A
38B
38C
38D
38E
38F
9X 0F9
391
392
393
394
395
396
397
398
399
39A
39B
39C
39D
39E
39F
AX 0FA
3A1
3A2
3A3
3A4
3A5
3A6
3A7
3A8
3A9
3AA
3AB
3AC
3AD
3AE
3AF
BX 0FB
3B1
3B2
3B3
3B4
3B5
3B6
3B7
3B8
3B9
3BA
3BB
3BC
3BD
3BE
3BF
CX 0FC
3C1
3C2
3C3
3C4
3C5
3C6
3C7
3C8
3C9
3CA
3CB
3CC
3CD
3CE
3CF
DX 0FD
3D1
3D2
3D3
3D4
3D5
3D6
3D7
3D8
3D9
3DA
3DB
3DC
3DD
3DE
3DF
EX 0FE
3E1
3E2
3E3
3E4
3E5
3E6
3E7
3E8
3E9
3EA
3EB
3EC
3ED
3EE
3EF
LLFX
0FF
3F1
3F2
3F3
3F4
3F5
3F6
3F7
3F8
3F9
3FA
3FB
3FC
3FD
3FE
3FF
__________________________________________________________________________
The present invention can also be implemented using combinational logic instead of a look-up table. FIG. 6 shows a block diagram for an encoder 200 for producing a rate 16/17 code with minimum Hamming weight of 7 and a run-length-limited constraint of 6 for the entire encoded sequence and 6 for each interleave in the sequence. Encoder 200 is divided into two parts, part A and part B. Part A consists of code tester (A) 202 and encoder (A) 204 and part B consists of code tester (B) 206 and encoder (B) 208.
Encoder (A) 204 receives the 8 most significant bits (D15 -D8) of a 16 bit input data word (D15:0) along input bus 220. These 8 bits are denoted as A7:0 in encoder (A) 204, which is shorthand for a string of 8 bits: A7 A6 A5 A4 A3 A2 A1 A0. Of the 8 bits received by encoder (A) 204, code tester (A) 202 receives the least significant 7 bits, denoted as WA6:0 in code tester (A) 202, along bus 222.
Code tester (A) 202 produces output TA 203 which is input to encoder (A) 204. Based on TA 203 and inputs A7:0, encoder (A) 204 produces 7 code bits Y6:0 on output bus 210. Encoder (A) 204 also produces three state variables S0, S1 and S2 and two part B bits WB8 and WB9.
Part B bits WB8 and WB9 are input to code tester (B) 206, along lines 216 and 218, respectively. Code tester (B) 206 also receives the least significant 8 bits (D7 -D0) of the input data word along input data bus 224. These bits are denoted as input bits WB7:0 in code tester (B) 206. Based on inputs WB7:0, WB8 and WB9, code tester (B) 206 produces an output TB 214 which is input to encoder (B) 208.
In addition to receiving TB 214, encoder (B) 208 receives state variables S0, S1 and S2 along lines 228, 230 and 232, respectively, and the least significant 8 bits (D7 -D0) of the input data word along input bus 226. Within encoder (B) 208, the least significant 8 bits of the input data word are denoted as B7:0. Based upon all of the input values, encoder (B) 208 produces 10 output code bits Z9:0 along output bus 212.
The combinational logic used by code tester (A) 202, encoder (A) 204, code tester (B) 206, and encoder (B) 208 is described below using the following symbols:
"|" represents a bitwise OR;
"&"0 represents a bitwise AND;
"+" represents an arithmetic sum;
"0" represents XOR; and
"X" represents the inverse of X.
In addition, in these equations, the subscript numbering notation is replaced by a single script notation. Thus, in the equations that follow, S0 is represented as SO, B1 is represented as B1 and so forth.
Code tester (A) 202 produces output TA 203 based upon inputs WA6:0 using the following equations:
______________________________________
UA0 = WA6 | WA5 | WA4 | WA3
Eq. 1
UA1 = WA3 | WA2 | WA1 | WA0
Eq. 2
UA2 = WA6 | WA4 | WA2 | WA0
Eq. 3
UA3 = WA5 | WA3 | WA1
Eq. 4
{ HWA = WA6+WA5+WA4+WA3+WA2+WA1+WA0
if (HWA>2)
UA4=1
else
UA4=0
} Eq. 5
TA = UA0 & UA1 & UA2 & UA3 & UA4
Eq. 6
______________________________________
Encoder (A) 204 produces output 210 (Y6:0) using input bits A7:0 and TA 203 in equations 7 through 29 below.
______________________________________
NH0 = A7 & A6 & A5 & A4 Eq. 7
NH8 = A7 & A6 & A5 & A4 Eq. 8
NL1 = A3 & A2 & A1 & A0 Eq. 9
NL2 = A3 & A2 & A1 & A0 Eq. 10
NL4 = A3 & A2 & A1 & A0 Eq. 11
NL5 = A3 & A2 & A1 & A0 Eq. 12
GA = A3&A2&A1&A0 Eq. 13
HA = (A6|A5 |A4)&(NL4 |NL1)
Eq. 14
JA = (A6|A5 |A4)&(NL5 |NL2)
Eq. 15
KA = (A6&A5&A4)&(A3&(A2|A1 |A0))
Eq. 16
LA = A3&(NH8 | NH0) Eq. 17
MA = (A6|A5 | A4)&A3
Eq. 18
YY6 = (KA&A2) | LA | (MA&(A7&A6))
Eq. 19
Y6 = (TA&A6) | (TA&( (GA&A6) |
(HA&A7) | (JA&(A7 | (A7&A5)))|YY6
Eq. 20
YY5 = (KA&A1) |LA| (MA&(A7|A6))
Eq. 21
Y5 = (TA&A5) | (TA&((GA&A5)|
(HA&A6) | (JA&(A6 | (A7&A5))) |YY5
Eq. 22
YY4 = (KA&A∩) | (LA&A7) | (MA&(A5|(A7&
A6))) Eq. 23
Y4 = (TA&A4) | (TA&((GA&A4) |
(HA&A4) | (JA&(A6 A4)) | YY4 ))
Eq. 24
Y3 = (TA&A3) | (TA&( GA|HA|JA
Eq. 25
Y2 = (TA&A2) | (TA&( GA| (HA&A2) |
KA | (LA&A2) | (MA&A6) ))
Eq. 26
Y1 = (TA&A1) | (TA&( GA|((HA|LA)&A0)
|
((JA|LA)&A1) | KA| (MA&A6)
Eq. 27
YY0 = (KA&A7) | (LA&A0) | (MA&A1)
Eq. 28
Y0 = (TA&A0) | (TA&( ((GA|KA)&A7)
|HA| (JA&A0) | YY0 ))
Eq. 29
______________________________________
Encoder (A) 204 produces state variables S0, S1 and S2 using the following equations:
______________________________________
S2 = A7 & TA Eq. 30
S1 = A7 & TA Eq. 31
S0 = TA Eq. 32
______________________________________
And encoder (A) 204 produces bits WB8 and WB9 using the following equations:
______________________________________
WB9 = S2|S0
Eq. 33
WB8 = S2|S1
Eq. 34
______________________________________
Code tester (B) 206 produces output TB 214 using input bits WB7:0 of the input data word and bits WB8 and WB9 from encoder (A) 204 in the following equations:
______________________________________
UB0 = WB9 | WB8 | WB7| WB6 |
Eq. 35
UB1 = WB8 | WB7 | WB6|
WB5 | WB4 | WB3| WB2
Eq. 36
UB2 = WB7 | WB6 | WB5|
WB4 | WB3 | WB2| WB1
Eg. 37
UB3 = WB3 | WB2 | WB1| WB0
Eq. 38
UB4 = WB7 | WB5 | WB3| WB1
Eq. 39
UB5 = WB8 | WB6 | WB4| WB2
Eq. 40
{ HWB =WB9+WB8+WB7+WB6+WB5+WB4+
WB3+WB2+WB1+WB0
if (HWB>3)
UB6= 1
else
UB6=0
} Eq. 41
TB = UB0 & UB1 & UB2 & UB3 &
Eq. 42
UB4 & UB5 & UB6
______________________________________
Encoder (B) 208 produces output bits 212 (Z9:0) using the least significant 8 bits of the input data word (B7:0), the three state variables S0, S1 and S2 and TB 214 in the following equations:
______________________________________
NH0 = B7&B6&B5&B4 Eq. 43
GB = (B7|B6|B5|B4) & (B3&B2&B1&B0)
Eq. 44
HB = ( TB&S2&(GB ) Eq. 45
JB = ( TB&S1&GB& ((B3&B2) | (B3&B2)) )
Eq. 46
KB = ( TB&S1&(B3 B2) ) Eq. 47
LB = ( TB&S0&B3&B2) Eq. 48
MB = ( TB&S0&B3&B2) Eq. 49
NB = ( TB&S0&GB&((B3&B2) | (B3&B23)) )
Eq. 50
Z9 = (TB&(S2 | S0)) Eq. 51
Z8 = (TB&(S1 | S2)) Eq. 52
ZZ7 = (MB&B7&B6&B4) | (NB&B7)
Eq. 53
Z7 = (TB&B7) | (TB&(ZZ7 | ((S2|S1)&GB)
| Eq. 54
HB|JB|KB|(LB&B7&B5) ))
ZZ6 = (MB&((B6 B4) | B7)) |
(NB&B7&B6&(B1|B0))
Z6 = (TB&B6) | (TB&(Z6|GB|HB|(KB&B2)
| Eq. 55
(LB&(B6 | B4 | (B7 B5))) ))
Eq. 56
ZZ5 = (MB&B4) | (NB&(B6 | (B5&B7) | (B1&B0)))
Eq. 57
Z5 = (TB&B5) | (TB&(Z5 | ((S2|S0)&GB)
| Eq. 58
HB|JB|(KB&B3)|(LB&B5&B4) ))
ZZ4 = (MB&((B7&B5&B4)|B6))|
Eq. 59
NB&(B4 |B3|(B7&B5)))
Z4 = (TB&B4) | (TB&(ZZ4|GB|JB|
Eq. 60
(LB&(B5 | (B7&B6&B4))) ))
ZZ3 = (KB&( (B2&(B6|B4|B1) ) |
Eq. 61
(B3&(B7|B6|B5|B4)))) | (LB&B6)
|NB
Z3 = (TB&B3) | (TB&(Z3 | (GB&B7)
(HB&B2) | (JB&(B7 | B5 | (B6 B4)))
Eq. 62
ZZ2 = (KB&((B7&B1&(B6|B4)) |B3)) |
Eq. 63
(LB&B1&B0) |MB|NB
Z2 = (TB&B2) | (TB&(ZZ2|(GB&B6) |
Eq. 64
(HB&B0) | (JB&(B7|B5|(NH0&B3))) ))
ZZ1A = (LB&((B1&B0) | (B1&B0)))|
Eq. 65
(MB&B1)|(NB&(B1|(B1&B0)))
ZZ1 = (KB&((B2&B5&B1&(B6|B4))|
Eq. 66
(B3&(B7|B6|B1|B0))))|ZZ1A
Z1 = (TB&B1) | (TB&(ZZ1 | (GB&B5) | (HB&(B6.v
ertline. Eq. 67
B3|B1))|(JB&(B7|B6|(NH0&B1)))
))
ZZ0A = (LB&B0) | (MB&B0) | (NB&(B0 | (B1&B0)))
Eq. 68
ZZ0 = (KB&((B2&(B7|B5|B1|B0))|
Eq. 69
(B3&(B7|B5|B1|(NH0&B0)))))|ZZ0A
Z0 = (TB&B0) | (TB&(Z0 | (GB&B4) |
Eq. 70
(HB&(B4 | (B2&B1&B0))) | (JB&B0) ))
______________________________________
The 7 output bits 210 (Y6:0) and the 10 output bits 212 (Z9:0) are concatenated together to form a 17 bit codeword.
FIG. 7 is a block diagram of a decoder 250 for decoding the codewords produced by encoder 200. Decoder 250 includes a part A and a part B, where part A includes code tester (A) 252 and decoder (A) 254, and part B includes code tester (B) 256 and decoder (B) 258.
The least significant 10 bits of each codeword (Zg9:0) are input to part B of decoder 250 along input bus 260. Code tester (B) 256 receives the same 10 code bits along input bus 262, but denotes the 10 bits as WB9:0. Code tester (B) 256 uses these input bits to produce output TB 264 using equations 35 through 42 described above. Thus, code tester (B) 256 contains the same combinational logic as code tester (B) 206 of FIG. 6. The code tester circuit 206 may be shared by the encoder (FIG. 6) and the decoder (FIG. 7).
______________________________________
P0 = (Z7 | (Z6 & Z5)) &(Z6 | Z5 | Z4)
Eq. 71
GZ = Z6 & Z4 & (Z7 | Z5)
Eq. 72
HZ = Z7 & Z6 & Z5 & Z4 Eq. 73
JZ, = Z7 & Z6 & Z5 & Z4 Eq. 74
KZ = Z7 & Z4 & (Z6 Z5) Eq. 75
LZ = P0 & ( (Z3 & (Z2 | (Z1 & Z0)))
| (Z3 & Z2) ) Eq. 76
MZ = P0 & (Z3 & Z2)
NZ = P0 & (Z3 & Z2 & (Z1 | Z0))
Eq. 77
Eq. 78
BB7 = (LZ&(Z7 | (Z6&Z5&Z3))) |
Eq. 79
(MZ&Z7&Z6&Z5&Z4) | (NZ&Z7)
B07 = BB7 | (GZ&Z3) | (JZ&Z3&Z2&Z1)
Eq. 80ine.
(KZ&((Z3,&Z2) | (Z5&Z3&Z1&Z0)))
BB6A= (LZ&Z3) | (MZ&Z7&Z4) |
Eq. 81
(NZ&Z6&Z5&(Z1 | Z0))
BB6 = BB6A | (KZ&((Z5&Z3&Z2) |
Eq. 82
(Z5&Z3&Z1&Z0)))
B06 = BB6 | (GZ&Z2) | (HZ&Z1&(Z3 | Z2))
Eq. 83
| (JZ&Z2 &Z1)
BB5A = (LZ&(Z7 | (Z6&Z4))) | (MZ&Z7&Zn4)
Eq. 84
| (NZ&( (Z7&Z4) | (Z6&Z5)))
BB5 = BSA | (KZ&((Z2&Z1 &Z0)&((Z6&Z3)))
Eq. 85
| Z5&Z3))))
B05 = BB5 | (GZ&Z1) | (JZ&Z3&Z2&Z1)
Eq. 86
BB4A= (LZ&(Z6&Z5 &Z4)) | (MZ&Z5)
Eq. 87
(NZ&Z4& (Z6|(Z7&Z1)))
BB4 = BB4A | (KZ&((Z6&Z3&Z1)
Eq. 88
(Z5&Z1&Z0)))
B04 = BB4 | (GZ&Z0) | (HZ&Z0&
Eq. 89
(Z3 | Z2)) | (JZ&Z2&(Z3 Z1))
BB3 = (LZ) | (NZ&Z5&Z4&Z1)
Eq. 90
B03 = BB3 | (HZ&Z3&Z2&Z1&Z0) |
Eq. 91
(JZ&Z3&Z2&Z1&Z0) | (KZ&Z5)
BB2 = (MZ) | (NZ&Z5&Z4&Z1)
Eq. 92
B02 = BB2 | (HZ&Z3) Eq. 93
(JZ&Z3&Z2&Z1&Z0) | (KZ&Z6)
BB1A = (LZ&(Z3&Z2&(Z1|Z0))) |
Eq. 94
(MZ&Z1) | (NZ&Z1&(Z7|Z6|Z0))
BB1 = BB1A | (KZ&((Z6&Z2&Z1) |
Eq. 95
(Z5&Z3&Z1&Z0)))
B01 = BB1 | (HZ&Z3&Z2&Z1&Z0) |
Eq. 96
(JZ&((Z3&Z2&Z1) | (Z3&Z0)))
BB0A = (LZ&Z0) | (MZ&Z0) |
Eq. 97
(NZ&Z0&(Z7|Z6|Z1))
BB0 = BB0A | (KZ&((Z6&Z0&((Z1&Z2) |
Eq. 98
(Z3&(Z1|Z2)) )) | (Z5&Z3&Z1&Z0)))
B00 = BB0 | (HZ&Z2) | (JZ&Z0)
Eq. 99
ZZ = Z9&Z8 Eq. 100
S2 = (Z9&Z8) | (ZZ&Z7&Z6&Z5)
Eq. 101
S1 = (Z9&Z8) | (ZZ&(Z7&(Z6 Z5)))
Eq. 102
S0 = (Z9&Z8) | ( ZZ&(Z7|(Z6&Z5)))
Eq. 103
B7 = ( ZZ & B07) | (ZZ & Z7)
Eq. 104
B6 = ( ZZ & B06) | (ZZ & Z6)
Eq. 105
B5 = ( ZZ & B05) | (ZZ & Z5)
Eq. 106
B4 = ( ZZ & B04) | (ZZ & Z4)
Eq. 107
B3 = ( ZZ & B03) | (ZZ & Z3)
Eq. 108
B2 = ( ZZ & B02) | (ZZ & Z2)
Eq. 109
B1 = ( ZZ & B01) | (ZZ & Z1)
Eq. 110
BO = ( ZZ & B00) | (ZZ & Z0)
Eq. 111
______________________________________
Code tester (A) 252 receives the 7 most significant bits of the codeword, which are represented as WA6:0 in code tester (A) 252, along input bus 276. Code tester (A) 252 uses equations 1 through 6 described above together with the input bits to produce output TA 278, which is provided to decoder (A) 254. Thus, code tester (A) 252 contains the same combinational logic as code tester (A) 202 of FIG. 6.
Decoder (A) 254 also receives the most significant 7 bits (Y6:0) of the codeword along input bus 280 and state variables S0, S1 and S2 from decoder (B) 258 along lines 266, 268, and 270, respectively. Decoder (A) 254 uses these input values to produce the 8 most significant bits (A7:0) of the recovered data word and an invalid codeword indicator FA along output bus 282 and line 284, respectively.
Invalid codeword indicator FA is simply the inverse of TA 278 from code tester (A) 252. Recovered data bits A7:0 are determined using the following equations:
______________________________________
GY = Y3&Y2&Y1 Eq. 112
HY = Y3&Y0&(Y2 Y1) Eq. 113
JY = Y3&Y2&(Y1 ee Y0) Eq. 114
KY = Y3&Y2&Y1 Eq. 115
LY = Y6&Y5&Y3 & (Y2|Y1)
Eq. 116
MY = Y3&KY&LY Eq. 117
A07 = (GY|KY)&Y0) | (HY&Y6) | (JY&Y6&(Y4.vertli
ne.Y5|Y1)) Eq. 118
| (LY&Y4) | (MY&(Y6|(Y4&Y2)))
A06 = (GY&Y6) | (HY&Y5) |
(JY&(Y5&(Y4|Y0))) | (MY&Y2)
A05 = (GY&Y5)| (HY&Y5&Y4) | (JY&Y6&Y4&((Y5&Y1)
|(Y5)) | (MY&(Y4&Y1))
A04 = (GY|HY)&Y4) | (JY&((Y5&Y4) |
Eq. 119
(Y4&Y0))) | (MY&(Y4&Y2))
Eq. 120
A03 = LY | MY Eq. 121
A02 = (HY&Y2) | (JY&Y0) | (KY&Y6) | (LY&Y2)
A01 = ((JY&Y1) | (KY&Y5) |
Eq. 122
(LY&Y1&Y0) | (MY&Y1&Y0)
Eq. 123
A00 = (HY&Y1) | (JY&Y0) | (KY&Y4)
| (LY&Y1&Y0) Eq. 124
S12 = S2 | S1 Eq. 125
A7 = (S2) | (S0 & A07) Eq. 126
A6 = ( S12 & Y6) | (S0 & A06)
Eq. 127
A5 = ( S12 & Y5) | (S0 & A05)
Eq. 128
A4 = ( S12 & Y4) | (S0 & A04)
Eq. 129
A3 = ( S12 & Y3) | (S0 & A03)
Eq. 130
A2 = ( S12 & Y2) | (S0 & A02)
Eq. 131
A1 = ( S12 & Y1) | (S0 & A01)
Eq. 132
A0 = ( S12 & Y0) | (S0 & A00)
Eq. 133
______________________________________
In general, the preferred embodiment includes a storage device 100 having a storage medium 102 and a write element 108 positioned adjacent the storage medium 102 to write information to the storage medium 102 in response to a write signal input. The device 100 also includes a data input 112 providing a plurality of data input bits to a first block encoder 152. The first block encoder 152 provides a first encoded data output to the write element 108 as a function of a portion of the data input 112. The first encoder also provides a state number output 156 as a function of the data input. The second encoder 154 also couples the data input 112 and provides a second encoded output to the write element 108 as a function of a portion of the data input 112 and as a function of the state number output 156. Further, the first and second encoder output may be provided to a PRML precoder 126 which responsively provides the write signal to the write element 108. Another aspect of the invention is for use with block decoders. In this aspect, storage device 100 includes read element 108 which reads information from storage medium 102 and responsively provides a read signal output. A first decoder 162 is coupled to the read element and provides a state number output 166 and a first decoded data output as a function of a portion of a read signal output from the read element 108. The first decoded output is provided to a system data output 114. A second decoder couples to the read element 108 and provides a second decoded data output 114 as a function of the read signal output and as a function of the state number output 166. The second decoded output is also provided to the data output 114. Further, a PRML detector 132 may also be provided between read element 108 and decoders 162 and 164.
Thus, the present encoder/decoder greatly reduces the number of entries in a table of the type used in encoding and decoding.
In general, the encoder/decoder provides a plurality of block encoding/decoding tables in which an output from one table is used as an input to another table. This allows the overall number of data entries to be reduced without sacrificing the constraints placed on the code. The encoder/decoder may be implemented as appropriate including software or hardware implementations. Further, the particular codes, number of tables, number of state, etc., may change for any particular application. The encoder/decoder may use other techniques as desired including algorithm based or adaptive data translation techniques. Aspects of the invention include the division of codewords into two unequal parts and implementation of state dependent encoding/decoding with a different number of states for each pair. Further, each part of the decoder input has the same length. The code tester can be used to reduce logic count because the input data pattern can be used directly as the codeword if it satisfies the code constraints. The code tester checks the constraints and sends a signal to the encoder if the input word directly satisfies the constraints.
It is to be understood that even though numerous characteristics and advantages of various embodiments of the present invention have been set forth in the foregoing description, together with details of the structure and function of various embodiments of the invention, this disclosure is illustrative only, and changes may be made in detail, especially in matters of structure and arrangement of parts within the principles of the present invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed. For example, the particular elements may vary depending on the particular application for the block encoder and decoder while maintaining substantially the same functionality without departing from the scope and spirit of the present invention. In addition, although the preferred embodiment described herein is directed to a storage device it will be appreciated by those skilled in the art that the teachings of the present invention can be applied to other systems, like data communication in general, without departing from the scope and spirit of the present invention. Various other codes may also be used, more than one encoding or decoding table may be linked together, additional or different state numbers may be used, the data provided to the encoders or decoders may be partitioned or may overlap as desired, etc.
Claims (24)
1. A communication channel, comprising:
a medium;
an output element to output information to the medium in response to received data encoded bits;
a data input having a plurality of data input bits;
a first encoder including a state number output and a first encoded data output which outputs encoded bits as a function of a first portion of bits from a plurality of data bits in an input data stream, the first encoded data output coupled to the output element; and
a second encoder including a second encoded data output which outputs data encoded bits as a function of a second portion of data bits from the plurality of data bits in the input data stream and as a function of the state number output, the second encoded data output coupled to the output element.
2. The communication channel of claim 1 wherein the first encoder comprises a first look-up table configured to map the first portion of bits into the first encoded data output and the state number output.
3. The storage device of claim 2 wherein the first table includes at most 28 ×7 data entries for each state number.
4. The communication channel of claim 1 wherein the first encoder comprises an algorithm responsively translating the first portion of bits into the first encoded output and the state number output.
5. The communication channel of claim 1 wherein the second encoder comprises a second look-up table configured to map the second portion of bits and the state number output into the second encoded data output.
6. The communication channel of claim 5 wherein the second table includes 28 ×10 data entries for each state number output and there are 3 state number outputs.
7. The communication channel of claim 1 wherein the second encoder comprises an algorithm responsively translating the second portion of bits and the state number output into the second encoded output.
8. The communication channel claim 1 wherein the first encoder and the second encoder include tables of codewords for the first and second encoded data outputs, the codewords selected to provide a desired minimum codeword energy.
9. The communication channel of claim 1 including a partial response maximum likelihood encoder coupled between the first and second encoded data outputs and the write signal input.
10. The communication channel of claim 9 wherein the partial response maximum likelihood encoder comprises a class 4 partial response precoder.
11. The communication channel of claim 1 wherein the state number output link between the first encoded data output and the second encoded data output to selectively constrain the output from the output element.
12. The communication channel of claim 1 wherein the medium comprises a storage medium and the output element comprises a head proximate the medium.
13. The communication channel of claim 12 wherein the storage medium comprises a disc.
14. A communication channel, comprising:
a medium;
an input element to receive information from the medium and responsively provide a received signal having a plurality of data bits;
a data output;
a first decoder responsively outputting a first decoded data output to the data output and a state number output as a function of a first portion of the plurality of data bits; and
a second decoder responsively outputting a second decoded data output to the data output as a function of a second portion of the plurality of data bits and as a function of the state number output.
15. The communication channel of claim 14 wherein the first decoder comprises a first look-up table configured to map the first portion of the plurality of data bits into the first decoded data output and the state number.
16. The communication channel of claim 15 wherein the first table includes 28 ×7 data entries for each state number output and there are 3 state numbers.
17. The communication channel of claim 14 wherein the second decoder comprises a second look-up table configured to map the second portion of the plurality of data bits and the state number into the second decoded data output.
18. The communication channel of claim 17 wherein the second table includes at most 28 ×10 data entries for each state number output and there are 3 state number outputs.
19. The communication channel of claim 14 wherein the decoder and the second decoder include tables of codewords for the first and second decoded data outputs, the codewords selected to provide a desired minimum codeword energy.
20. The communication channel of claim 14 including a partial response maximum likelihood decoder coupled between the input element and the first and second decoders.
21. The communication channel of claim 14 wherein the first decoder comprises an algorithm responsively translating the first portion of bits into the state number output and the first decoded data output.
22. The communication channel of claim 14 wherein the second decoder comprises an algorithm responsively translating the state number output and the second portion of bits into the second decoded data output.
23. The communication channel of claim 14 wherein the medium comprises a storage medium and the input element comprises a head positioned proximate the medium.
24. The communication channel of claim 23 wherein the storage medium comprises a disc.
Priority Applications (7)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US09/020,874 US6111834A (en) | 1997-08-11 | 1998-02-09 | Data storage system having efficient block code implementation |
| KR1020007001416A KR100571743B1 (en) | 1997-08-11 | 1998-05-14 | A communication channel |
| CNB988080664A CN1157713C (en) | 1997-08-11 | 1998-05-14 | Data Storage System with Efficient Block Code Scheme |
| DE19882603T DE19882603T1 (en) | 1997-08-11 | 1998-05-14 | Data storage system with effective block code implementation |
| JP2000506647A JP2001512880A (en) | 1997-08-11 | 1998-05-14 | Data storage system with efficient block code implementation |
| GB0001559A GB2343056B (en) | 1997-08-11 | 1998-05-14 | Data storage system having efficient block code implementation |
| PCT/US1998/009814 WO1999008264A1 (en) | 1997-08-11 | 1998-05-14 | Data storage system having efficient block code implementation |
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US5473997P | 1997-08-11 | 1997-08-11 | |
| US09/020,874 US6111834A (en) | 1997-08-11 | 1998-02-09 | Data storage system having efficient block code implementation |
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| Publication Number | Publication Date |
|---|---|
| US6111834A true US6111834A (en) | 2000-08-29 |
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ID=26693994
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| US09/020,874 Expired - Fee Related US6111834A (en) | 1997-08-11 | 1998-02-09 | Data storage system having efficient block code implementation |
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|---|---|
| US (1) | US6111834A (en) |
| JP (1) | JP2001512880A (en) |
| KR (1) | KR100571743B1 (en) |
| CN (1) | CN1157713C (en) |
| DE (1) | DE19882603T1 (en) |
| GB (1) | GB2343056B (en) |
| WO (1) | WO1999008264A1 (en) |
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| US6480125B2 (en) | 2000-06-09 | 2002-11-12 | Seagate Technology Llc | Method and apparatus for efficient encoding of large data words at high code rates |
| US6501802B1 (en) * | 1998-01-30 | 2002-12-31 | 3Com Corporation | Digital silence for a PCM data communication system |
| US20030011919A1 (en) * | 2001-07-09 | 2003-01-16 | Bane Vasic | Method and apparatus for suppressing low frequency content in digital data |
| US20050040976A1 (en) * | 2003-08-13 | 2005-02-24 | Seagate Technology Llc | DC-free code design with increased distance between code words |
| US20060007024A1 (en) * | 2004-07-07 | 2006-01-12 | Seagate Technology Llc | High rate running digital sum-restricted code |
| CN1320794C (en) * | 2002-11-13 | 2007-06-06 | 上海芯华微电子有限公司 | Single step, high-speed method and device for contract convolutional coding |
| US20090097759A1 (en) * | 2007-10-12 | 2009-04-16 | Himax Technologies Limited | Image processing device and method for compressing and decompressing images |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6185640B1 (en) * | 1998-06-19 | 2001-02-06 | Philips Electronics North America Corporation | Minimal frame buffer manager allowing simultaneous read/write access by alternately filling and emptying a first and second buffer one packet at a time |
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| US5627843A (en) * | 1995-02-23 | 1997-05-06 | Seagate Technology, Inc. | Correcting up to two disc drive read errors and detecting the occurrence of more than two read errors |
| US5640286A (en) * | 1995-05-08 | 1997-06-17 | Western Digital Corporation | Disk drive with error code embedded sector identification |
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| US6501802B1 (en) * | 1998-01-30 | 2002-12-31 | 3Com Corporation | Digital silence for a PCM data communication system |
| US6480125B2 (en) | 2000-06-09 | 2002-11-12 | Seagate Technology Llc | Method and apparatus for efficient encoding of large data words at high code rates |
| US20030011919A1 (en) * | 2001-07-09 | 2003-01-16 | Bane Vasic | Method and apparatus for suppressing low frequency content in digital data |
| US6909385B2 (en) | 2001-07-09 | 2005-06-21 | Seagate Technology Llc | Method and apparatus for suppressing low frequency content in digital data |
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| US20050040976A1 (en) * | 2003-08-13 | 2005-02-24 | Seagate Technology Llc | DC-free code design with increased distance between code words |
| US6961010B2 (en) | 2003-08-13 | 2005-11-01 | Seagate Technology Llc | DC-free code design with increased distance between code words |
| US20060007024A1 (en) * | 2004-07-07 | 2006-01-12 | Seagate Technology Llc | High rate running digital sum-restricted code |
| US7002492B2 (en) | 2004-07-07 | 2006-02-21 | Seagate Technology Llc | High rate running digital sum-restricted code |
| US20090097759A1 (en) * | 2007-10-12 | 2009-04-16 | Himax Technologies Limited | Image processing device and method for compressing and decompressing images |
| US8014612B2 (en) * | 2007-10-12 | 2011-09-06 | Himax Technologies Limited | Image processing device and method for compressing and decompressing images |
Also Published As
| Publication number | Publication date |
|---|---|
| GB2343056A (en) | 2000-04-26 |
| DE19882603T1 (en) | 2000-10-26 |
| CN1306659A (en) | 2001-08-01 |
| GB0001559D0 (en) | 2000-03-15 |
| JP2001512880A (en) | 2001-08-28 |
| KR100571743B1 (en) | 2006-04-18 |
| WO1999008264A1 (en) | 1999-02-18 |
| GB2343056B (en) | 2001-09-12 |
| CN1157713C (en) | 2004-07-14 |
| KR20010022814A (en) | 2001-03-26 |
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